Opérateurs de transmutation et théorème de Paley–Wiener associés à un opérateur aux dérivées et différences sur [formula omitted

Abstract

We consider a singular differential-difference operator Λ on the real line. We construct a pair of integral transforms which transmute Λ into the first derivative operator d/ dx . We use these transmutation operators to develop a new commutative harmonic analysis on the real line corresponding to the operator Λ.